Bone Parallelogram Connection Translations and Parenting
There are two simple solutions to it:
What both rigs have in common:

boss and helper are children with offset of main. That puts them into local space and prevents flipping. If ever the rig has to do a looping this becomes relevant.

bar is a child of boss.

neck 1 is a child of bar with offset.


1. Two simple constraints.
This one works if the bones are really parallel and have the same length (copied). Helper has a Copy Rotation Constraint and rotates in sync with boss.
Bar has a Locked Track Constraint pointing to helper. Locked Tracks only rotate around a locked axis and are therefore more stable than a Track To. They won't flip.
Now you can rotate boss and everything will follow.




2. One slightly more complicated constraint
This one will work regardless of lengths and rotations as long as it can function mechanically. Good for rigging excavators. It has an additional bone, target, which is a child of helper with no offset.
This time, bar has an IK Constraint pointing to helper, chain length 2. boss and helper kind of need a rename since now it's helper who gets to be animated. bar and boss will follow.
But you could just as well turn bar around, parent it to helper, put the target on top of boss and do the IK chain the other way around.


A third solution would be to let main be a duplicate of bar, maybe form a complete parallelogram with the 4 bones and give bar a copy rotation constraint to main but it's not really needed.